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In nonstationary environments, it is difficult to apply traditional genetic algorithms (GAs) because they use strong selection pressure and lose the diversity of individuals rapidly. We propose a GA with neutral variation that can track environmental changes. The idea of this GA is inspired by Kimura's neutral theory (1983). The scheme of this GA allows neutral characters, which do not directly affect the fitness with respect to environments, thus increasing the diversity of individuals. In order to demonstrate the properties of this GA, we apply it to a permutation problem called the ladder-network, of which the imposed alignment on the output changes regularly. We show that the GA with neutral variation can adapt better to environmental changes than a traditional GA.